In class today, someone asked whether the sample statistic
and the population parameter need to focus on the same concept (such as
the mean). Let me take a stab here at explaining why the answer to this
question is a big, fat "YES."

Let's imagine that there are two researchers, A and
B. They both take a sample from a population. Researcher A uses the sample
data to compute the mean because he/she wants to make a guess as to the
value of the population mean. Thus, the statistic and the parameter both
deal with the mean. Researcher B takes the sample data and computes the
variance, but he/she is really interested in the population's median.
Here, the statistic and the parameter deal with different concepts.

Now, your job is to tell me which of these two researchers
(A or B) was completely inebriated!